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What is the maximum acceleration of the ...

What is the maximum acceleration of the particle doing the SHM `gamma=2sin[(pit)/2phi]` where gamma is in cm?

A

`(pi)/(2)cm//s^(2)`

B

`(pi^(2))/(2)cm//s^(2)`

C

`(pi)/(4)cm//s^(2)`

D

`(pi)/(4)cm//s^(2)`

Text Solution

Verified by Experts

The correct Answer is:
B
`y=2 sin ((pit)/(2)+phi)`
Comparing the equation with the standard equation
`y=A sin (omegat+phi)`
So `A=2 cm, omega=(pi)/(2)`
Acceleration of particle is
`a=omega^(2)x" "["numerically"]`
At `x=+A, a=a_("max")
`therefore" "a_("max")=omega^(2)A=((pi)/(2))^(2)xx2`
`=2xx(pi^(2))/(4)=(pi^(2))/(2)cm//s^(2)`
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